hft trading

8/6/2019 HFT Trading

1/66Electronic copy available at: http://ssrn.com/abstract=1641387

HIGH FREQUENCY TRADING AND ITS

IMPACT ON MARKET QUALITY

Jonathan A. Brogaard

Northwestern University

Kellogg School of Management

Northwestern University School of [email protected]

July 16, 2010

I would like to thank my advisors, Tom Brennan, Robert Korajczyk, Robert McDonald, An-

nette Vissing-Jorgensen for the considerable amount of time and energy they spent discussing this

topic with me. I would like to thank Nasdaq OMX for making available the data used in this

project. Also, I would like to thank the many other professors and Ph.D. students at Northwestern

Universitys Kellogg School of Management and at Northwesterns School of Law for assistance

on this paper. Please contact the author before citing this preliminary work.

1


2/66


3/66Electronic copy available at: http://ssrn.com/abstract=1641387

1 Introduction

1.1 Motivation

On May 6, 2010 the Dow Jones Industrial Average dropped over 1,000 points in

intraday trading in what has come to be known as the flash crash. The next

day, some media blamed high frequency traders (HFTs; HFT is also used to refer

to high frequency trading) for driving the market down (Krudy, June 10, 2010).

Others in the media blamed the temporary withdrawal of HFTs from the market as

causing the precipitous fall (Creswell, May 16, 2010).1 HFTs have come to make

up a large portion of the U.S. equity markets, yet the evidence of their role in the

financial markets has come from news articles and anecdotal stories. The SEC has

also been interested in the issue. It issued a Concept Release regarding the topicon January 14, 2010 requesting feedback on how HFTs operate and what benefits

and costs they bring with them (Securities and Commission, January 14, 2010).

In addition, the Dodd Frank Wall Street Reform and Consumer Protection Act

calls for an in depth study on HFT (Section 967(2)(D)). In this paper I examine the

empirical consequences of HFT on market functionality. I utilize a unique dataset

from Nasdaq OMX that distinguishes HFT from non-HFT quotes and trades. This

paper provides an analysis of HFT behavior and its impact on financial markets.

Such an analysis is necessary since to ensure properly functioning financial mar-

kets the SEC and exchanges must set appropriate rules for traders. These rules

should be based on the actual behavior of actors and not on hearsay and anecdotalstories. It is equally important that institutional and retail investors understand

whether or not they are being manipulated or exploited by sophisticated traders,

such as HFT.

This paper studies HFT from a variety of viewpoints. First, it describes the

activities of HFTs, showing that HFTs make up a large percent of all trading and

that they both provide liquidity and demand liquidity. Their activities tend to be

stable over time. Second, it examines HFT strategy and profitability. HFTs gen-

erally engage in a price reversal strategy, buying after price declines and selling

after price gains. They are profitable, making around $3 billion each year on trad-

ing volume of $30 trillion dollars traded. Third, it considers the impact of HFTs

on the market, focusing on three areas - liquidity, price discovery, and volatility.

HFTs increase market liquidity: using a variety of Hasbrouck measures, I find that

HFTs appear to add to the efficiency of the markets. Finally, I find that HFTs tend

to decrease volatility.

1To date, the true cause of the flash crash has not been determined.

3


4/66

Given these results, HFT appear to be a new form of market makers. HFTs

appear to make markets operate better (i.e. increase liquidity and price efficiency,and reduce volatility) for all market participants.

HFT is a recent phenomenon. Tradebot, a large player in the field who fre-

quently makes up over 5% of all trading activity, states that the strategy of HFT

has only been around for the last ten years (starting in 1999). Whereas only re-

cently an average trade on the NYSE took ten seconds to execute, (Hendershott

and Moulton, 2007), now some firms entire trading strategy is to buy and sell

stocks multiple times within a mere second. The acceleration in speed has arisen

for two main reasons: First, the change from stock prices trading in eighths to

decimalization has allowed for more minute price variation. This smaller price

variation makes trading with short horizons less risky as price movements are inpennies not eighths of a dollar. Second, there have been technological advances

in the ability and speed to analyze information and to transport data between lo-

cations. As a result, a new type of trader has evolved to take advantage of these

advances: the high frequency trader. Because the trading process is the basis by

which information and risk become embedded into stock prices it is important to

understand how HFT is being utilized and its place in the price formation process.

1.2 Definitions

To date, there lacks a clear definition for many of the terms in rapid trading and

in computer controlled trading. Even the Securities and Exchange recognizes this

and says that high frequency trading does not have a settled definition and mayencompass a variety of strategies in addition to passive market making (Secu-

rities and Commission, January 14, 2010). High frequency trading is a type of

strategy that is engaged in buying and selling shares rapidly, often in terms of mil-

liseconds and seconds. This paper takes the definition from the SEC: HFT refers

to, professional traders acting in a proprietary capacity that engages in strategies

that generate a large number of trades on a daily basis (Securities and Commis-

sion, January 14, 2010). By some estimates HFT makes up over 50% of the total

volume on equity markets daily (Securities and Commission, January 14, 2010;

Spicer, December 2, 2009).

Other terms of interest when discussing HFT include pinging and algorith-mic trading.

The SEC defines pinging as, an immediate-or-cancel order that can be used

to search for and access all types of undisplayed liquidity, including dark pools

and undisplayed order types at exchanges and ECNs. The trading center that

receives an immediate-or-cancel order will execute the order immediately if it has

4


5/66

available liquidity at or better than the limit price of the order and otherwise will

immediately respond to the order with a cancelation (Securities and Commission,January 14, 2010). The SEC goes on to clarify, [T]here is an important distinction

between using tools such as pinging orders as part of a normal search for liquidity

with which to trade and using such tools to detect and trade in front of large

trading interest as part of an order anticipation trading strategy (Securities and

Commission, January 14, 2010).

A type of trading that is similar to HFT, but fundamentally different is algorith-

mic trading. Algorithmic Trading is defined as the use of computer algorithms

to automatically make trading decisions, submit orders, and manage those orders

after submission (Hendershott and Riordan, 2009). Algorithmic and HFT are

similar in that they both use automatic computer generated decision making tech-nology. However, they differ in that algorithmic trading may have holding periods

that are minutes, days, weeks, or longer, whereas HFT by definition hold their

position for a very short horizon and try and to close the trading day in a neutral

position. Thus, HFT must be a type of algorithmic trading, but algorithmic trading

need not be HFT.

2 Literature Review

HFT has received little attention to date in the academic literature. This is be-

cause until recently the concept of HFT did not exist. In addition, data to conduct

research in this area has not been available. The only academic paper regardingHFT is one by Kearns, Kulesza, and Nevmyvaka (2010), and this paper shows

that the maximum amount of profitability that HFT can make based on TAQ data

under the implausible assumption that HFT enter every transaction that is prof-

itable. The findings suggest that an upper bound on the profits HFT can earn per

year is $21.3 billion. Although my research is the first to look at the impact of

HFT on the stock market, it touches on a variety of related fields of research, the

most relevant being algorithmic trading.

2.1 Algorithmic Trading

In principal algorithmic trading is similar to HFT except that the holding period

can vary. It is also similar to HFT in that data to study the phenomena are difficultto obtain. Nonetheless several papers have studied algorithmic trading (AT).

Hendershott and Riordan (2009) use data from the firms listed on the Deutsche

Boerse DAX. They find that AT supply 50% of the liquidity in that market. They

find that AT increase the efficiency of the price process and that AT contribute

5


6/66

more to price discovery than does human trading. Also, they find a positive re-

lationship between AT providing the best quotes for stocks and the size of thespread. Regarding volatility, the study finds little evidence between any relation-

ship between it and AT.

Hendershott, Jones, and Menkveld (2008) utilize a dataset of NYSE electronic

message traffic, and use this as a proxy for algorithmic liquidity supply. The

time period of their data surrounds the start of autoquoting on NYSE for different

stocks and so they use this event as an exogenous instrument for AT. The study

finds that AT increases liquidity and lowers bid-ask spreads.

Chaboud, Hjalmarsson, Vega, and Chiquoine (2009) look at AT in the foreign

exchange market. Like Hendershott and Riordan (2009), they find no evidence

of there being a causal relationship between AT and price volatility of exchangerates. Their results suggest human order flow is responsible for a larger portion of

the return variance.

Together these papers suggest that algorithmic trading as a whole improves

market liquidity and does not impact, or may even decrease, price volatility. This

paper fits in to this literature by decomposing the AT type traders into short-

horizon traders and others and focusing on the impact of the short-horizon traders

on market quality.

2.2 Theory

There is an extant literature in theoretical asset pricing. Of these papers only a

handful try to understand what the impact on market quality will be of havinginvestors with different investment time horizons. Two papers directly address

the scenario when there are short and long term investors in a market: Herd on

the Street: Informational Inefficiencies in a Market with Short-Term Speculation

(Froot, Scharfstein, and Stein, 1992); and Short-Term Investment and the Infor-

mational Efficiency of the Market (Vives, 1995).

Froot, Scharfstein, and Stein (1992) find that short-term speculators may put

too much emphasis on some (short term) information and not enough on funda-

mentals. The result being a decrease in the informational quality of asset prices.

Although the paper does not extend its model in the following direction, a de-

crease in the informational quality suggests a decrease in price efficiency and anincrease in volatility.

Vives (1995) obtains the result that the market impact of short term investors

depends on how information arrives. The informativeness of asset prices is im-

pacted differently based on the arrival of information, with concentrated arrival

of information, short horizons reduce final price informativeness; with diffuse ar-

6


7/66

rival of information, short horizons enhance it (Vives, 1995). The theoretical

work on short horizon investors suggest that HFT may be beneficial to marketquality or may be harmful to it.

3 Data

3.1 Standard Data

The data in this paper comes from a variety of sources. It uses in standard fash-

ion CRSP data when considering daily data not included in the Nasdaq dataset.

Compustat data is used to incorporate firm characteristics in the analysis.

3.2 Nasdaq High Frequency Data

The unique data set used in this study has data on trades and quotes on a group

of 120 stocks. The trade data consists of all trades that occur on the Nasdaq ex-

change, excluding trades that occurred at the opening, closing, and during intraday

crosses. The trade date used in this study includes those from all of 2008, 2009

and from February 22, 2010 to February 26, 2010. The trades include a millisec-

ond timestamp at which the trade occurred and an indicator of what type of trader

(HFT or not) is providing or taking liquidity.

The Quote data is from February 22, 2010 to February 26, 2010. It includes

the best bid and ask that is being offered by HFT firms and by non-HFT firms at

all times throughout the day.

The Book data is from the first full week of the first month of each quarterin 2008 and 2009, September 15 - 19, 2008, and February 22 - 26, 2010. It

provides the 10 best price levels on each side of the market that are available on

the Nasdaq book. Along with the standard variables for limit order data, the data

show whether the liquidity is provided by a HFT or a non-HFT, and whether the

liquidity was displayed or hidden.

The Nasdaq dataset consists of 26 traders that have been identified as engag-

ing primarily in high frequency trading. This was determined based on known

information regarding the different firms trading styles and also on the firms

website descriptions. The characteristics of HFT firms that are identified are the

following: They engage in proprietary trading; that is, the firm does not havecustomers but instead trades its own capital. The HFT use sophisticated trading

tools such as high-powered analytics and computing co-location services located

near exchanges to reduce latency. The HFT engage in sponsored access providers

whereby they have access to the co-location services and can obtain large-volume

discounts. HFT tend to use OUCH protocol whereas non-HFT tend to use RASH.

7


8/66

The HFT firms tend to switch between long and short net positions several times

throughout the day, whereas non-HFT labeled firms rarely switch from long toshort net positions on any given day. Orders by HFT firms are of a shorter time

duration than those placed by non-HFT firms. Also, HFT firms normally have a

lower ratio of trades per orders placed than for non-HFT firms.

Firms that others may define as HFT are not labeled as HFT firms here if they

satisfy one of the following: firms like Lime Brokerage and Swift Trade who pro-

vide direct market access and other powerful trading tools to its customers, who

are likely engaging in HFT and thus are likely HFT traders but are not labeled so;

proprietary trading firms that are a desk of a larger, integrated firm, like Goldman

Sachs or JP Morgan; an independent firm that is engaged in HFT activities, but

who routes its trades through a MPID of a non-HFT type firm; firms that engagein HFT activities but because they are small are not considered in the study as

being labeled a HFT firm.

The data is for a sample of 120 Nasdaq stocks where the ticker symbols are

listed in Table 1. These sample stocks were selected by a group of academics. The

stocks consist of a varying degree of market capitalization, market-to-book ratios,

industries, and listing venues.

4 Descriptive Statistics

Before entering the analysis section of the paper, as HFT data has not been iden-

tified before, I first provide the basic descriptive statistics of interest. I look at liq-uidity and trading statistics of the HFT sample and show they are typical stocks,

I then compare the firm characteristics to the Compustat database and show they

are on average larger firms, but otherwise a relatively close match to an average

Compustat firm. Finally, I provide general statistics on the percent of the mar-

ket trades in which HFT are involved, considering all types of trades, supplying

liquidity trades, and demanding liquidity trades.

Table 2 describes the 120 stocks in the Nasdaq sample data set. These statistics

are taken for the five trading days from February 22 to February 26, 2010. This

table shows that these stocks are quite average and provide a reasonable subsample

of the market. The price of the stocks is on average 39.57 and ranges between 4.6

and 544. The daily trading volume on Nasdaq for these stocks averages 1.064

million shares, and ranges from as small as 2,000 shares to 14 million shares.

This is done on average over 5,150 trades, whereas some stock trade just 8 times

on a given day while others trade as many as 59,799 times. The 120 stocks are

quite liquid. Quoted half-spreads are calculated when trades occur. the average

8


9/66

Table1:ListofStocks

AA

AAPL

ABD

ADBE

AGN

AINV

AMAT

AMED

AMGN

AMZN

ANGO

APOG

ARCC

AXP

AYI

AZZ

BARE

BAS

BHI

BIIB

BRCM

BRE

BW

BXS

BZ

CB

CBEY

CBT

CBZ

CCO

CDR

CELG

CETV

CHTT

CKH

CMCSA

CNQR

COO

COST

CPSI

CPWR

CR

CRI

CRVL

CSCO

CSE

CSL

CTRN

CTSH

DCOM

DELL

DIS

DK

DOW

EBAY

EBF

ERIE

ESRX

EWBC

FCN

FFIC

FL

FMER

FPO

FRED

FULT

GAS

GE

GENZ

GILD

GLW

GOOG

GPS

HON

HPQ

IMGN

INTC

IPAR

ISIL

ISRG

JKHY

KMB

KNOL

KR

KTII

LANC

LECO

LPNT

LSTR

MAKO

MANT

MDCO

MELI

MFB

MIG

MMM

MOD

MOS

MRTN

MXWL

NC

NSR

NUS

NXTM

PBH

PFE

PG

PNC

PNY

PPD

PTP

RIGL

ROC

ROCK

ROG

RVI

SF

SFG

SJW

SWN

9


10/66

quoted half-spread of 1.82 cents is comparable to large and liquid stocks in other

markets. The average trade size, in shares is 139.6. The average depth of theinside bid and ask, measured by summing the depth at the bid and at the ask times

their respective prices, dividing by two and taking the average per day, is $71,550.

Table 2: Summary Statistics. Summary statistics for the HFT dataset from February 22,

2010 to February 26, 2010.

Variable Mean Std. Dev. Min. Max.

Price 39.573 60.336 4.628 544.046

Daily Trading Volume (Millions) 1.064 2.137 0.002 14.857

Daily Number of Trades per Day 5150.983 7591.812 8 59799

Quoted Half Spread (cents) 1.838 4.956 0.5 42.5

Trade Size 139.617 107.631 37 1597

Depth (Thousand Dollars) 71.55 196.421 1.161 2027.506

N 600

Table 3 describes the 120 stocks in the HFT database compared to the Com-

pustat database. The table shows that the HFT database is on average larger then

the average Compustat firm. The Compustat firms consist of all firms in the Com-

pustat database with data available and that have a market capitalization of greater

than $10 million in 2009. The Compustat database statistics include the firms that

are found in the HFT database. The data for both the Compustat and the HFTfirms are for firms fiscal year end on December 31, 2009. If a firms year end is

on a different date, the fiscal year-end that is most recent, but prior to December

31, 2009, is used. Whereas the average Compustat firm has a market capitaliza-

tion of $2.6 billion, the average HFT database firm has a market capitalization of

$17.59 billion. However the sample does span a large size variation of firms, from

the very small with a market capitalization of only $80 million, to the the very

large with market capitalization of $175.9 billion. Compustat includes many very

small firms that reduce the mean market capitalization, making the HFT sample

be overweighted with larger firms. The market-to-book ratio also differs between

Compustat and the HFT sample. Whereas HFT have a mean market-to-book of2.65, the Compustat data has one of 10.9. Based on industry, the HFT sample is a

relatively close match to the Compustat database. The industries are determined

based on the Fama-French 10 industry designation from SIC identifiers. The HFT

database tends to overweight Manufacturing, Telecommunications, Healthcare,

and underweight Energy and Other. The HFT firms are all listed on the NYSE or

10


11/66

Nasdaq exchange, with half of the firms listed on each exchange. Whereas about

one-third of Compustat firms are listed on other exchanges. 2 The HFT databaseprovides a robust variety of industries, market capitalization, and market-to-book

values.

Table 4 looks at the prevalence of HFT in the stock market. It captures this

in a variety of ways: the number of trades, shares, and dollar-volume that have a

HFT involved compared to trades where no HFT participates. The table provides

summary statistics for the involvement of HFT traders in the market. Three differ-

ent statistics are calculated for each split of the data. The column Trades reports

the number of trades, Shares reports the number of shares traded, and Dollar

reports the dollar value of those shares traded. Panel A - HFT Involved In Any

Trade splits the data based on whether a HFT was involved in any way in a trade ornot. The results show that HFT make up over 77% of all trades. HFT tend to trade

in smaller shares as per-share traded they make up just under 75%. Finally, based

on a dollar-volume basis of trade, they make up 73.8% of the trading volume.

The next two panels separate HFT transactions into what side of the trade they

are on based on liquidity. Panel B - HFT Involved As Liquidity Taker groups

trades into HFT only when the HFT is demanding the liquidity in the transaction.

HFT takes liquidity in 50.4% of all trades, worth a dollar amount of just about the

same percentage of all transactions on a dollar basis. They make up only 47.6% of

shares trading, suggesting they provide liquidity in stocks that are slightly higher

priced.

Panel C - HFT Involved As Liquidity Supplier groups trades into HFT only

when the HFT is supplying the liquidity in the transaction. The amount of liquidity

supplied is only slightly more than that demanded by HFT at 51.4% of all trades

having a liquidity supplier being a HFT. Based on number of shares this value

falls to 50.8% of all shares traded; and based on dollar-volume, it drops to 45.5%

of all trades.

5 HFT Strategy

Before analyzing HFT impact on market quality, it is insightful to understand

more about what drives HFT activity. To research this, I use an ordered logit

regression to show their trading strategy is heavily dependent on past returns. I

further identify that they engage in a price reversal strategy, whereby they tend to

2Comparing Compustat firms that are listed on NYSE or Nasdaq reduces the number of firms

to 5050 with an average market capitalization of $3.46 billion, and with the industries more closely

matching those in the HFT dataset.

11


12/66

Table3:HFTSa

mplev.Compustat.Thistable

comparestheHFT-identifieddatasetwiththeCompustatdataset.

The

CompustatdataconsistsofallfirmsintheCompustatdatabasewithamarketcapita

lizationof$10millionormore.

The

industriesarecategorizedbasedontheFama-French

10industrygroups.

HFT

Dataset

CompustatDataset

mean

sd

min

max

me

an

sd

min

max

MarketCap.(m

illions)

17588.24

37852.38

80.602

197012.3

2613.01

12057.34

10.001

322334.1

Market-to-Book

2.65

3.134

-11.779

20.040

10.919

598.126

-2489.894

44843.56

Industry-Non-Durables

.0333

.180

.034

.181

Industry-Durables

.025

.156

.014

.120

Industry-Manu

facturing

.1667

.374

.071

.257

Industry-Energy

.0083

.091

.049

.217

Industry-High

Tech

.1583

.366

.124

.330

Industry-Telec

om.

.05

.218

.024

.153

Industry-Wholesale

.0917

.289

.058

.235

Industry-HealthCare

.15

.358

.080

.272

Industry-Utilit

ies

.0333

.180

.034

.183

Industry-Other

.2833

.452

.509

.499

Exchange-NYSE

.5

.502

.288

.453

Exchange-Nas

daq

.5

.502

.322

.467

Exchange-Oth

er

0

0

.388

.487

Observations

120

8260

12


13/66

Table 4: HFT Aggregate Activity. The table provides summary statistics for the involve-

ment of HFT traders in the market. Three different statistics are calculated for each split

of the data. The column Trades reports the number of trades, Shares reports the number

of shares traded, and Dollar reports the dollar value of those shares traded. Panel A - HFT

Involved In Any Trade splits the data based on whether a HFT was involved in any way

in a trade or not. Panel B - HFT Involved As Liquidity Taker groups trades into HFT only

when the HFT is demanding the liquidity in the transaction. Panel C - HFT Involved As

Liquidity Supplier groups trades into HFT only when the HFT is supplying the liquidity

in the transaction.

Panel A - HFT Involved In Any Trade

Type of Trader Trades

(Sum)

Trades (%) Shares

(Sum)

Shares (%) Dollar

(Sum)

Dollar (%)

HFT 2,387,851 77.3% 477,944,435 74.9% $19,427,424,121 73.8%

Non HFT 702,739 22.7% 160,337,476 25.1% $6,879,817,754 26.2%

Total 3,090,590 100.0% 638,281,911 100.0% $26,307,241,875 100.0%

Panel B - HFT Involved As Liquidity Taker

HFT 1,556,766 50.4% 303,971,478 47.6% $13,169,044,493 50.1%

Non HFT 1,533,824 49.6% 334,310,433 52.4% $13,138,197,383 49.9%

Total 3,090,590 100.0% 638,281,911 100.0% $26,307,241,875 100.0%

Panel C - HFT Involved As Liquidity Supplier

HFT 1,588,157 51.4% 324,221,557 50.8% $11,959,264,046 45.5%

Non HFT 1,502,433 48.6% 314,060,354 49.2% $14,347,977,829 54.5%Total 3,090,590 100.0% 638,281,911 100.0% $26,307,241,875 100.0%

13


14/66

buy stocks at short-term troughs and they tend to sell stocks at short-term peaks.

This is true regardless of whether they are supplying or demanding liquidity. Also,HFT tend to trade in larger, value firms, with lower volume and lower spreads and

depth. Finally, based on their trading activities at the aggregate level I estimate

they earn approximately $3 billion a year.

5.1 Investment Strategy

HFT do not readily share their trading strategies. However, the anecdotal stories

of HFT firms suggest they have essentially replaced the role of market makers by

providing liquidity and a continuous market into which other investors can trade.

What is known regarding HFT is that they tend to buy and sell in very short

time periods. Therefore, rather than changes in firm fundamentals, HFT firmsmust be basing their decision to buy and sell from short term signals such as stock

price movements, spreads, or volume.

I begin the analysis by performing an all-inclusive ordered logit regression

into the potentially important factors; thereafter I analyze the promising strategies

in more detail. There are three decisions a HFT firm makes at any given moment:

Does it buy, does it sell, or does it do nothing. This decision making process

occurs continuously. I model this setting by using a three level ordered logit. The

ordered logit is such that the lowest decision is to sell, the middle option is to do

nothing, and the highest option is to buy.

Before getting to the ordered logit, I summarize the theoretical reason for why

an ordered logit is appropriate in this setting, as first discussed by Hausman, Lo,and MacKinlay (1992).

HFT trading behavior consist of a sequence of actions Z(t1), Z(t2), . . . , Z (t)observed at regular time intervals t0, t1, t2, . . . , t. Let Z

k be an unobservable

continuous random variable where

Zk = X

k + k, E[k|Xk] = 0, k i.n.i.d. N(0, 2k) (1)

where i.n.i.d. stands for the assumption that the ks are independent but notidentically distributed, and Xk is a q 1 vector of predetermined variables that

sets the conditional mean of Z

k . Whereas Hausman, Lo, and MacKinlay (1992)deal with tick by tick stock price data, the scenario in this paper deals with HFT

trade behavior data that is aggregated into ten second intervals. Therefore, the

subscripts are used to denote ten second period, not transaction time.

The essence of the ordered logit model is the assumption that observed HFT

behavior Zk are related to the continuous variable Z

k in the following mapping:

14


15/66

Zk =

s1 if Z

k A1,s2 if Z

k A2,...

...

sm if Z

k Am,

where the sets Aj form a partition of the state space of Zk . The partition

will have the properties that =mj=1 Aj and AiAj = for i = j, and the sjs

are the discrete values that comprise the state space of Zk. The ordered logitspecification allows an investigator to understand the link between and andrelate it to a set of economic variables used as explanatory variables that can be

used to understand the HFT trading strategy. In this application the sjs are Sell,Do Nothing, Buy. Note, the observable actions could also be split into size, for

example, Sell 1000 + shares, Sell 500 - 1000, etc., but I restrict the partition tothese three natural breaks. The alternative fine tuned separation, for instance, by

subdividing the buys and selling into the number of shares exchanged, is beyond

the needs of this analysis.

I assume the error terms in ks in equation 1 are conditionally independently,but not identically, distributed, conditioned on the Xks and the other explanatoryvariables, Wk, that are omitted from equation 1, which allows for heteroscedas-ticity in 2k.

The conditional distribution of observed return changes Zk, conditioned on

Xk and Wk, is determined by the partition boundaries calculated from the orderedlogit regression. As stated in Hausman, Lo, and MacKinlay (1992), for a Gaussian

k, the conditional distribution is

P(Zk = si|Xk, Wk)

= P(X

k + k Ai|Xk, Wk)

=

P(X

k + k 1|Xk, Wk) ifi = 1

P(i1 < X

k + k i|Xk, Wk) if1 < i < m,P(m1 < X

k + k|Xk, Wk) ifi = m,(2)

15


16/66

=

(1

X

kk ) ifi = 1

(iX

k

k) (

i1X

k

k) if1 < i < m,

1 (m1X

k

k) ifi = m,

(3)

where () is the standard normal cumulative distribution function.The intuition for the ordered logit model is that the probability of the type of

behavior by the HFT is determined by where the conditional mean lies relative to

the partition boundaries. Therefore, for a given conditional mean X

k, shifting theboundaries will alter the probabilities of observing each state, Sell, Do Nothing,

or Buy. The order of the outcomes could be reversed with no real consequence

except for the coefficients changing signs as the ordered logit only takes advantageof the fact there is some natural ordering of the events. The explanatory variables

then allow one to analyze the different effects of relevant economic variables to

understand HFT behavior . As the data determines where the partition boundaries

the ordered logit model creates an empirical mapping between the unobservable

state space and the observable state space. Here, the empirical relationshipbetween HFT behavior can be analyzed with respect to the economic variables Xkand Wk.

I divide the time frames in to ten second intervals throughout the trading day.3 For each ten second interval I utilize a variety of independent variables. The

regression I run is as follows:

HF Ti,t = +111 retlagi,010 +1222 depthbidlagi,010+2333 depthasklagi,010 +3444 spreadlagi,010+4555 tradeslagi,010 5666 dollarvlagi,010

Each explanatory variable and its associated beta coefficient has a subscript

0-10. This represents the number of lagged time periods away from the event

occurring in the time t dependent variable. Subscript 0 represents the contempo-

3I also tried other time intervals, such as 250 milliseconds, one second and 100 second periods.The results from these alternative suggestions are similar in significance to the results presented

in that where a ten second period shows significance, so does the one second interval for ten

lagged periods worth, and similarly where ten lagged ten second intervals show significance, so

does the one lagged one hundred second interval. The ten second intervals has been adopted after

attempting a variety of alterations but finding this one the best for keeping the results parsimonious

and still being able to uncover important results.

16


17/66

raneous value for that variable. For example, retlag0 represents the return for the

particular stock during time period t. And, the return for time period t is defined asretlagi,0 = (pricei,tpricei,t1)/pricei,t1. Thus the betas represent row vectorsof 1x11 and the explanatory variables column vectors of 11x1. Depthbid is theaverage time weighted best bid depth for stocki in that time period. Depthask isthe average time weighted best offer depth for stocki in that time period. Spreadis the average time weighted spread for company i in that time period, wherespread is the best ask price minus the best bid price. Trades is the number ofdistinct trades that occurred for company i in that time period. DollarV is thedollar-volume of shares exchanged in transactions for company i in that time pe-riod. The dependent variable, HF T, is -1, 0 or 1. It takes the value -1 if during

that ten second period HFT were on net selling shares for stock i, it is zero if theHFT performed no transaction or its buys and sell exactly canceled, and it is 1 ifon net HFT were buying shares for stock i.

From this ordered logit model one may expect to see a variety of potential

patterns. A handful of different strategies have been suggested in which HFT

engage. For instance, momentum trading, price reversal trading, trading in high

volume markets, or trading in high spread markets. It could be they base their

trading decisions on the srpead and so the Spread variables would have a lot ofpower in explaining when HFT buy or sell. If HFTs are in general momentum

traders, then I would expect to see them buy after prices rise, and to sell after

prices fall. If HFTs are price reversal traders, then i would expect to observe them

buying when prices fall and to sell when prices are rising. Table 5 shows the

results.

The results reported in table 5 are the marginal effects at the mean for the

ordered probit. From the ordered logit regressions summarized results in table 5,

there is sporadic significance in all but one place, the lagged values of company

is stock returns. There is a strong relationship with higher past returns and thelikelihood the HFT will be selling (and with low past returns and the likelihood

the HFT will be buying). There is some statistical significance in other locations,

however no where is it consistent like that of the return coefficients. This suggests

that past spread size, depth, and volume are not primary factors in HFT trading

decisions. Of the strategies discussed above, these results are consistent with aprice reversal trading strategy. To further understand this potential price reversal

strategy I focus on analyzing the lag returns influence on HFTs trading behavior.

It appears that HTF engage in a price reversal strategy. To analyze this further,

I analyze the HFT buy and sell logits separately, focusing on the lagged returns

surrounding a HFT firms buying or selling stocks, analyzing the differences in

17


18/66


19/66


20/66

Table 6: Regressions of the Sell decision, split based on Liquidity Type. This table

reports the results from running a logit with dependent variable equal to 1 if (1) HFT on

net sell in a given ten second period, (2) HFT on net sell and supply liquidity, and (3)

HFT on net sell and demand liquidity, and 0 otherwise. Firm fixed effects are used. The

reported coefficients are the marginal effects at the mean.

(1) (2) (3)

HFT Sell - ALL HFT Sell - Supply HFT Sell - Demand

retlag0 4.925 16.35 -16.48

(0.66) (3.69) (-8.38)retlag1 5.145 -0.934 7.594

(3.13) (-0.96) (9.80)

retlag2 5.230 1.179 4.619

(3.87) (1.44) (5.54)

retlag3 6.521 2.684 4.276

(5.87) (4.03) (6.03)

retlag4 4.881 1.234 4.209

(4.13) (1.60) (5.41)

retlag5 4.194 2.038 2.498

(3.82) (2.46) (3.45)

retlag6 5.098 2.278 2.989

(4.91) (3.65) (4.26)

retlag7 3.380 0.497 3.439

(3.84) (0.83) (4.21)

retlag8 0.923 0.0277 1.087

(0.99) (0.04) (1.68)

retlag9 2.521 0.270 2.610

(2.53) (0.43) (3.14)

retlag10 0.351 -0.854 1.603

(0.39) (-1.28) (2.22)

N 1377798 1377798 1343177Marginal effects; tstatistics in parentheses p < 0.05, p < 0.01, p < 0.001

20


21/66

The last column in table 7 has as the dependent variable a one if HFT were

on net taking liquidity from the market and buying during the ten second intervaland a zero otherwise. There is still some statistical significance from the ten past

return periods, but only in time periods 0 and 3 - 6. The signs for the lag returns

are negative as expected, except for the contemporaneous period return, which is

large and positive. Like in the HFT Sell - Demand scenario, it is not clear from

this logit model how to interpret this.

The results in table 6 and 7 show that HFT are engaged in a price reversal

strategy. This is true whether they are supplying liquidity or demanding it.

5.1.1 Front Running

A potential investing strategy of which HFT have been claimed to be engaged inis front running. That is, the anecdotal evidence charges HFT with detecting when

other market participants hope to move a large number of shares in a company and

that the HFT enters into the same position just before the other market participant.

It is in this context where the HFT pinging, as defined in the Definitions section,

and the SECs concern with it apply. That is, some claim HFT ping stock prices

to detect large orders being executed. If they detect a large order coming through

they may increase their trading activity. The result of such an action by the HFT

would be to drive up the cost for the non-HFT market participant to execute the

desired transaction.

To see whether or not this is occurring on a systematic basis I perform the

following exercise: For each stock over the database time series I create twentybins based on trade size for trades initiated by non-HFT. Each bin has roughly

the same number of observations. Next, I look at the average percent of trades

that were initiated by a HFT for different number of trades prior to the non-HFT

initiated trade (for prior trades 1 - 10).

I graph the results in figure 5. The x-axis is the 20 different non-HFT initiated

trade size bins; the y-axis is the fraction of trades for different non-HFT trade size

bins for different prior trade periods that were initiated by a HFT; the z-axis is the

different prior trade periods.

The figure suggests front running by HFT before large orders is not systemati-

cally occurring. In fact, it appears that larger trades, relative to each stock, tend tobe preceded by fewer HFT initiated trades. The non-HFT trades that are preceded

by the highest number of HFT initiated trades are those that are small and those

are of moderate size. Also, it is interesting that the immediately preceding trades

tend to have fewer HFT initiated trades than those further out. As will be shown

later, trades initiated by one type of market participant have a greater probability

21


22/66

Table 7: Regressions of the Buy decision, split based on Liquidity Type. This table

reports the results from running a logit with dependent variable equal to 1 if (1) HFT on

net buy in a given ten second period, (2) HFT on net buy and supply liquidity, and (3)

HFT on net buy and demand liquidity, and 0 otherwise. Firm fixed effects are used. The

reported coefficients are the marginal effects at the mean.

(1) (2) (3)

HFT Buy - ALL HFT Buy - Supply HFT Buy - Demand

retlag0 -2.793 -48.10 53.48

(-0.37) (-14.21) (18.93)retlag1 -6.490 -4.910 -0.874

(-3.87) (-4.25) (-0.69)

retlag2 -5.763 -4.533 -1.408

(-4.44) (-4.38) (-1.80)

retlag3 -7.460 -4.257 -2.906

(-6.29) (-6.80) (-2.89)

retlag4 -6.291 -2.802 -3.202

(-5.25) (-3.75) (-3.84)

retlag5 -6.384 -2.572 -3.023

(-6.34) (-3.32) (-4.32)

retlag6 -6.110 -3.042 -2.766

(-6.14) (-4.28) (-3.85)

retlag7 -3.260 -2.001 -1.022

(-3.13) (-2.67) (-1.45)

retlag8 -2.274 -1.553 -0.226

(-2.43) (-2.50) (-0.28)

retlag9 -2.770 -1.513 -1.395

(-2.77) (-2.08) (-2.01)

retlag10 -2.049 -1.908 0.445

(-2.26) (-2.88) (0.67)

N 1377798 1366278 1377798Marginal effects; tstatistics in parentheses p < 0.05, p < 0.01, p < 0.001

22


23/66

Figure 1: HFT Front Running. The graph shows the percent of trades initiated by HFT

for different prior time periods that precede different size non-HFT initiated trades. The

x-axis is the 20 different non-HFT initiated trade size bins; the y-axis is the fraction of

trades for different non-HFT trade size bins for different prior trade periods that wereinitiated by a HFT; the z-axis is the different prior trade periods.

23


24/66

of being preceded by the same type of market participant.

5.1.2 HFT Market Activity

In addition to understanding the trading behavior of HFT at the trade by trade

level, it is informative to understand what drives HFT to trade in certain stocks

on certain days. Table 8 shows the variation in HFT market makeup in different

stock on different days. Panel A is the percent of trading variation of non-HFT and

HFT in a certain stock on a given day. Panel B is the percent of trading variation of

HFT trading and non-HFT in supplying liquidity for a particular stock on a given

day. Panel C is the percent of trading variation of HFT trading and non-HFT in

demanding liquidity for a particular stock on a given day.

Panel A shows that HFTs share of the market varies a great deal depending onthe stock and the day. Its percent of all trades varies from 10.8% to 93.6% based

on number of trades. They average being involved in 61.8% of all trades, which

compared to the numbers seen in the descriptive statistics from table 4, suggests

that they trade more in stocks that trade frequently, as they make up 77% of all

trades in the entire market.

Panel B looks at HFT supplying liquidity. HFT supply liquidity in 35.5% of

trades in the average stock per day. This number is substantially smaller than the

50% they were found to supply in the market as a whole in table 4. Thus, HFT

must supply liquidity in stocks that trade more frequently. Also, notice the wide

variation in the supply of liquidity, in some stocks they provide no liquidity, while

in others they supply 74%.Panel C looks at HFT demanding liquidity. They demand liquidity in 39.6% of

trades in the average stock per day. So HFT must be taking liquidity in stocks that

trade more frequently. Also, the HFT demand for liquidity varies substantially

ranging from 3.6% to 79.9%, but less than when they supply liquidity.

The results in table 8 show there is a large variation in the degree HFT trading

in different stocks over time, the next step is to consider which determinants result

in HFT increasing or decreasing their activity.

5.1.3 HFT Market Activity Determinants

Table 9 examines which determinants drive HFT trading. I perform an OLS re-gression, with the dependent variable being the percent of share volume, in which

HFT were involved in for a given company on a given day. I run the following

regression:

24


25/66

Table 8: Summary statistics 1 This table shows the variation in HFT market makeup.

Panel A is the percent of trading variation of non-HFT and HFT in a certain stock on a

given day. Panel B is the percent of trading variation of HFT trading and non-HFT in

supplying liquidity for a particular stock on a given day. Panel C is the percent of trading

variation of HFT trading and non-HFT in demanding liquidity for a particular stock on a

given day.

Panel A - HFT Involved In A Stock

Trades Shares

Type of Trader Mean Median Std.

Dev.

Min Max Mean Median Std.

Dev.

Min Max

HFT 61.8% 64.0% 18.25 10.8% 93.6% 58.4% 59.4% 17.99 7.8% 90.9%

Non HFT 39.3% 37.1% 19.24 6.4% 92.2% 42.7% 41.6% 18.83 9.1% 93.1%

Total 100.0%100.0% 100.0%100.0%

Panel B - HFT Involved In A Stock As Liquidity Supplier

HFT 36.8% 35.5% 15.99 0% 74.4% 33.4% 32.7% 14.54 0.2% 66.4%

Non HFT 64.1% 65.3% 16.63 25.6% 100.0%67.5% 67.9% 15.13 33.6% 100.0%

Total 100.0%100.0% 100.0%100.0%

Panel C - HFT Involved In A Stock As Liquidity Taker

HFT 39.6% 40.3% 16.43 3.6% 79.9% 37.8% 37.7% 16.49 2.6% 78.9%

Non HFT 61.1% 60.3% 16.70 20.1% 96.4% 62.8% 62.7% 16.73 21.1% 97.4%

Total 100.0%100.0% 100.0%100.0%

25


26/66

Hi,t = + MCi i + MBi i + NTi,t i,t +

NVi,t i,t + Depi,t i,t + V oli,t i,t + ACi,t i,t,

where i is the subscript representing the firm, t is the subscript for each day, His the percent of share volume in which HFT are involved out of all trades, MC isthe log market capitalization as of December 31, 2009, MB is the market to bookratio as of December 31, 2009, which is winsorized at the 99th percentile, NT isthe number of non HFT trades that occurred, scaled by market capitalization, N Vis the volume of non HFT dollars that were exchanged, scaled by market capital-

ization, Dep is the average depth of the bid and of the ask, equally weighted, V olis the ten second realized volatility summed up over the day, AC is the absolutevalue of the Durbin-Watson score minus two from a regression of returns over the

current and previous ten second period.

Table 9 reports the standardized regression coefficients. That is, instead of

running the typical OLS regression on the regressors, the variables, both depen-

dent and independent, are de-meaned, and are divided by their respective standard

deviations so as to standardize all variables. The coefficients reported can be un-

derstood as signaling that when there is a one standard deviation change in an

independent variable, the coefficient is the expected change in standard deviations

that will occur in the dependent variable. This makes the regressors underlyingscale of units irrelevant to interpreting the coefficients. Thus, the larger the coef-

ficient, the more important its role in impacting the dependent variable.

The results show that market capitalization is very important and has a posi-

tive relationship with HFT market percent. The market to book ratio is slightly

statistically significant, but with a very small negative coefficient, suggesting HFT

tend to slightly prefer value firms. Also statistically significant and with moderate

economically significant is the dollar volume of non HFT trading, which is inter-

preted as HFT preferring to trade when there is less volume, all else being equal.

The spread and depth variables are statistically significant and both have medium

economically significance. HFT prefer to trade when there is less depth and lower

spreads between bids and asks, all else being equal. Volatility, autocorrelation,and the number of non HFT trades are not statistically significant.

26


27/66

Table 9: Determinants of HFT Percent of the Market This table has as the dependent

variable the percent (in dollar volume) of trades involving a HFT for a given stock on a

given day.

(1)

Economic Impact

Market Cap. 0.722

(19.51)Market / Book -0.063

(-2.13)

$ of Non HFT Volume -0.138

(-3.82)

Average Spread -0.111

(-3.88)

Average Depth -0.132

(-4.79)

Volatility -0.031

(-1.07)Autocorrelation -0.017

(-0.62)

# of Non HFT Trades 0.042

(0.98)

Constant

(2.54)

Observations 590

Adjusted R2 0.575

Standardized beta coefficients; tstatistics in parentheses

p < 0.05,

p < 0.01,

p < 0.001

27


28/66

5.1.4 HFT Market Activity Time Series

A concern surrounding the May 6 flash crash was that the regular market par-

ticipants, such as HFT, stopped trading. Although the database I have does not

include the May 6, 2010 date, it does span 2008 and 2009, which were volatile

times in U.S. equity markets. To see whether HFT percent of market trades varies

significantly from day to day, and especially around time periods when the U.S.

market experienced large losses, I look at each trading day and count what frac-

tion of trades in which HFT were involved. The results are shown in figure 2.

There are three graphs. The first is a time series of the fraction of trades HFT

were involved in during 2008 and 2009. The second graph looks at the fraction of

shares in which HFT were involved during this period. The final graph looks at

the fraction of dollar volume in which HFT were involved during this period. Ineach graph there are three lines. The line labeled All HFT represents the frac-

tion of exchanges in which HFT were involved either as a liquidity provider or a

liquidity taker; the line labeled HFT Liquidity Supplied represents the fraction

of transactions in which HFT were providing liquidity; the line HFT Liquidity

Demanded represents the fraction of trades in which HFT were demanding liq-

uidity. All three graphs have minimal volatility among the three measures. Espe-

cially of note, there is no abnormally large drop, or increase, in HFT participation

occurring in September of 2009, when the U.S. equity markets were especially

volatile.

5.2 Profitability

HFT engage in a price reversal strategy and they make up a large portion of the

market. Given their trading amount a question of interest is how profitable is their

behavior. HFT have been portrayed as making tens of billions of dollars from

other investors. Due to the limitations of the data, I can only provide an estimate

of the profitability of HFT. The HFT labeled trades come from many firms, but I

cannot distinguish which HFT firm is buying and selling at a given time. Also,

recall the dataset only contains Nasdaq trades. Therefore, there will be many other

trades that occur that the dataset does not include. Nasdaq makes up about 20%

of all trades and so 4 out of every 5 trades are not part of the data set.

I consider all HFT to be one trader. I take all the buys and sells at the respec-

tive prices of the HFT and calculate how much money was spent on purchases

and received from sales. HFT tend to switch between being net long and net short

throughout the day, but at the end of the day they tend to hold very few shares.

With these considerations in mind, I can calculate an estimate of the total prof-

28


29/66

Figure 2: Time Series of HFT Market Participation The first graph is a time series of

the fraction of trades HFT where involved in during 2008 and 2009. The second graphlooks at the fraction of shares in which HFT were involved. The final graph looks at the

fraction of dollar volume in which HFT were involved. In each graph three lines appear.

One line represents whether HFT were involved as either a liquidity provider or a liquidity

taker; another line represents transactions in which HFT were providing liquidity; the final

line represents when HFT were demanding liquidity.

30

40

50

60

70

80

01 Jan 08 01 Jul 08 01 Jan 09 01 Jul 09 01 Jan 10sas_date

HFT Liquidity Demanded Trades All HFT Trades

HFT Liquidity Supplied Trades

20

40

60

80


HFT Liquidity Demanded Shares All HFT Shares

HFT Liquidity Supplied Shares

30

40

50

60

70

80


HFT Liquidity Demanded DVolume All HFT DVolume

HFT Liquidity Supplied DVolume

29


30/66

itability of these 26 firms. As many stocks do not end the day with an exact net

zero buying and selling by HFT, I take any excess shares and assume they weretraded at the mean price of that stock for that day. The result of this exercise is

that on average, per day, HFT make $298,113.1 from the 120 stocks in my sample

on trades that occur on Nasdaq.

The above number substantially underestimates the actual profitability of HFT.

First, the 120 stocks have a combined market capitalization of $2,110,589.3 (mil-

lion), whereas all compustat firms combined market capitalization is $17,156,917.3

(million), and so I should multiply the profitability by 8.13, raising the per day

HFT profitability from all stocks to $2,423,659.5 per day. The other large factor

to be incorporated is that Nasdaq trades make up approximately 20% of all trades,

so assuming HFT trade on other exchanges as they do on Nasdaq, the previousnumber should be multiplied by five. Thus the estimated daily profit of these 26

firms is $12,118,297.5. Per year that is $3,029,574,380. Although this is a large

absolute number, relatively it is small, especially given that HFT trade around $30

trillion annually.

There is no adjustment made for transaction costs yet. However, such costs

will be negligible, the reason being that when HFT provide liquidity they receive

a rebate from the exchange, for example Nasdaq offers $.20 per 100 shares for

which traders provided liquidity, but this is only for large volume traders like the

HFT. On the other hand, Nasdaq charges something like $.25 per 100 shares for

which trades take liquidity. As the amount of liquidity demanded is slightly less

than the liquidity supplied by HFT, these two values practically cancel themselves

out.

Figure 3 displays the time series of HFT profitability per day. The graph is a

five day-moving average of profitability of HFT per day for the 120 firms in the

dataset. Profitability varies substantially from day to day, even after smoothing

out the day to day fluctuations.

To try to understand what drives the changes in profitability per day I look

at the determinants for what stocks on different days are the most profitable. I

regress the profitability on several potentially important variables, the same ones

used in the regression to determine HFT percent of the market. I run the following

standardized regression (to obtain the economic impact):

Profiti,t = + Hi,t i,t + MCi i + MBi i + N Ti,t i,t +

N Vi,t i,t + Depi,t i,t + V oli,t i,t + ACi,t i,t,

30


31/66

Figure 3: Time Series of HFT Profitability Per Day. The figure shows the 5-day moving

average profitability for all trading days in 2008 and 2009 for trades in the HFT data set.

Profitability is calculated by aggregating all HFT for a given stock on a given day and

compaing the cost of shares bought and the revenue from shares sold. For any end-of-dayimbalance the required number of shares are assumed traded at the average share price for

the day in order to end the day with a net zero position in each stock.

1000000

0

10

00000

2000000

3000000

$Pro

fitPerDay


31


32/66

where all variables are defined as before, and the dependent variable Profit

takes on three different definitions. The results are displayed in Table 10. In thefirst column Profit is defined as the profit per HFT share traded averaged overstock i on day t; in the second column it is the amount of money HFT madefor stock i on day t; in the third column it is the number of HFT shares tradedfor stock i on day t. The second and third regression decompose the parts ofthe first regressions dependent variable. Again, the reported coefficients have

been standardized so that the coefficient value represents a one standard deviation

movement in a particular variables impact on Profit.The Profit per HFT Share Traded regression has no statistically or economi-

cally significant variables and has a negative r-squared. The second regression,

with the dependent variable as profits, has two coefficients that are statisticallysignificant. Autocorrelation and Volatility. Autocorrelation has a smaller coeffi-cient and is negative, implying the less predictable price movements in a stock the

more profitable is that stock for HFT. The V olatility measure has a large positiveeconomic impact and is highly statistically significant.

The third regression, HFT shares traded, has three statistically significant and

economically significant variables. MarketCap. is positive with a coefficient of0.21, the AverageDepth coefficient is positive and has a coefficient of 0.098,and the V olatility coefficient, which also has a positive relationship with thedependent variable, shows the largest coefficient magnitude of 0.622.

The results in this section have shown that HFT engage in a price reversal

trading strategy, that HFT tend to trade more in large stocks with relatively low

volume with narrow spreads and depth. Also, HFT are profitable, making approx-

imately $3 billion a year, and that the profitability is driven by volatility. Next, I

investigate the role HFT play in demanding and supplying liquidity.

6 Market Quality

The following section analyzes HFT impact on market quality. Market quality

refers to liquidity, price discovery, and volatility. Each analysis uses different

techniques to study the relationship between HFT and each type of market quality.

6.1 HFT Liquidity

Liquidity supply and demand in the microstructure literature refers to which side

of the transaction entered the marketable order and which side had a limit order

in place that was executed. The side with the limit order is the liquidity supplier,

and the marketable order side is the liquidity taker. In this section I look at the de-

32


33/66

Table 10: Determinants of HFT Profits Per Stock Per Day The dependent variable for

the first column is defined as the profit per HFT share traded averaged over each stock i

on day t; in the second column it is the amount of money HFT made for each stock on

each day; in the third column it is the number of HFT shares traded.

Profit per HFT Share Traded Profits HFT Shares Traded

HFT Percent -0.087 -0.024 0.062

(-1.04) (-0.40) (1.42)

Market Cap. -0.015 -0.059 0.210

(-0.16) (-0.86) (4.20)

Market / Book 0.014 -0.003 0.013

(0.23) (-0.07) (0.43)

$ of Non HFT Volume -0.058 0.019 -0.073

(-0.76) (0.36) (-1.90)

Average Spread -0.004 -0.015 0.000

(-0.06) (-0.35) (0.01)

Average Depth -0.009 -0.008 0.098

(-0.16) (-0.19) (3.33)

Volatility 0.038 0.359

0.622

(0.67) (8.67) (20.70)

Autocorrelation -0.033 -0.078 -0.036

(-0.62) (-1.97) (-1.24)

# of Non HFT Trades 0.027 -0.025 0.031

(0.29) (-0.41) (0.69)

Constant

(0.96) (1.45) (-3.66)

Observations 360 590 590

Adjusted R2 -0.014 0.111 0.532

Standardized beta coefficients; tstatistics in parentheses p < 0.05, p < 0.01, p < 0.001

33


34/66

scriptive statistics of how HFT demand liquidity, then I examine how they supply

liquidity, finally I analyze how much liquidity they provide in the quotes and thebook, not just for trades.

6.1.1 HFT Liquidity Demand

The results in table 4 show that liquidity is demanded by HFT in 50.4% of all

trades. This section will analyze how HFT initiated trades tend to behave com-

pared to non-HFT trades. HFT tend to demand liquidity in similar dollar size

trades as do non HFT. There appears to be clustering in trades, whereby if a previ-

ous trade is a buy, it is much more likely the next trade will also be a buy, and the

same is true for sales, and this clustering is stronger for HFT than for Non-HFT.

Trades that either proceed a HFT or follow a HFT tend to occur more quicklythan those proceeding or following a non-HFT. As trade size increases, the time

between trade decreases, and this is true regardless of the size of the firm. Finally,

HFT demands are quite consistent across the day, but they make up a significantly

smaller portion of trades at the opening and close of the trading day.

Table 11 looks at the percent of all transactions for different size trades, in

dollar terms, and with different HFT and non-HFT liquidity providers and de-

manders. The first column of Table 11 reports the fraction of trading volume for

different combinations of HFT firms and non-HFT firms as liquidity providers

and takers. For small trades, those worth less than $1,000 HFT are not as involved

as Non HFT, this is consistent with the previous results that show HFT tended to

trade more in stocks with large market caps, which typically have stock prices inthe double digits. Most trades occur in the value range of $1,000 to $4,999. The

HFT in two of their three categories are the most engaged in these transactions.

HFTs share of trades engaged in falls in the $5,000 to $14,999 category, except

for when they are demanding liquidity. In the $30,000 plus category of trades,

HFT provide the least amount of liquidity, but tend to demand the most. This sug-

gest that HFT are liquidity takers in large trades and liquidity providers in small

shares, which is consistent with the theory that HFT are concerned with informed

traders in big trades.

The previous table analyzed the frequency of different types of trades, the

next table examines the conditional frequency and occurrence of different types oftrades. Table 12, similar to that in Biais, Hillion, and Spatt (1995) and Hendershott

and Riordan (2009), provides evidence on the clustering of HFT trades in trade

sequences. In the table, H stands for HFT and N stands for non-HFT. The first

letter in the rows for Panel A and B is who is demanding liquidity at Time t-

1. The second letter in these two panels is who is demanding liquidity at time

34


35/66

Table 11: HFT Volume by Trade-size Category. This table reports dollar-volume par-

ticipation by HFT and non-HFT in 5 dollar-trade size categories. The first letter in the

column labels represents the liquidity seeking side. The second letter in the column labelsrepresents the passive party. H represents a HFT, N represents a non-HFT.

Type of Liquidity Taker and Liquidity Supplier

Dollar Size Categories HH HN NH NN Total N

0-1,000 21.5% 25.7% 25.3% 27.5% 100.0% 245,401

1,000-4,999 25.8% 24.5% 28.3% 21.5% 100.0% 1,473,047

5,000-14,999 23.7% 27.0% 26.3% 23.0% 100.0% 940,63415,000-29,999 25.1% 25.9% 26.2% 22.8% 100.0% 308,102

30,000 + 17.4% 32.2% 19.6% 30.7% 100.0% 141,609

Total 24.4% 25.8% 26.8% 23.0% 100.0% 3,108,793

N 757,864 803,177 833,883 713,869 3,108,793

35


36/66

t. Panel A reports the unconditional frequency of observing HFT and non-HFT

trades. Seeing a HFT demand liquidity in time t-1 followed by a HFT demandingliquidity in time t is as common as seeing any other time t-1, t sequence. Panel

B reports the conditional frequency of observing HFT and non-HFT trades after

observing trades of other participants. In Panel B, the columns are whether the

liquidity taker is buying (B) or selling (S). The first letter represents what the

liquidity taker is doing in the time t-1 trade. The second letter represents what the

liquidity taker is doing in the time t trade. In column and row headings t indexes

trades, not time. The results suggest that one tends to see liquidity demanders

purchase shares follow a previous trade of a liquidity demander purchasing shares,

and the same with sales, regardless of what type of trader was demanding the

liquidity. The clustering affect is stronger, in both buying and selling, for HFTdemanders than it is for Non-HFT demanders.

Panel C provides conditional probabilities based on the previous trades size

and type of trader. The rows represent the type of trader taking liquidity at time t-

1, either H for HFT or N for non-HFT. In addition, the rows are further partitioned

based on the size of the trade, measured by the dollar size of shares exchanged in

the t-1 trade. 1 represents a trade of size $0 -$999; 2 represents a trade of size

$1,000 - $4,999; 3 represents a trade of size $5,000 - $14,999; 4 represents a trade

of size $15,000 - $29,999; and 5 represents a trade of size greater than $30,000.

The columns identify who was the liquidity demander at time t (H or N) and is

further partitioned along the size categories discussed above. The results show

that trades of size and type of liquidity demander are highly dependent on the

previous trade type. HFT tend to trade with HFT, and the larger the dollar size of

a trade the higher the likelihood the next trade will be large.

The next set of results regarding type of trader initiating trading looks at the

time between trades. Table 13 reports the average time between trades depen-

dent on different trade characteristics. All times reported are in seconds. Panel

A reports the average amount of time between two trades, two HFT liquidity de-

manding trades, and two non-HFT liquidity demanding trades, and between a

trade where the t-1 trade was initiated by a trader who was a HFT, or a non-HFT.

Both trades when the liquidity demander is HFT at both t-1 and t, and when HFT

is the liquidity demander at t-1, regardless of who demands liquidity at time t, aremore rapidly executed.

Panel B provides the average amount of time between two different trade or-

derings and total dollar-volume and per trade dollar-volume categories. The first

two columns in Panel B is for some trade type at t-1 and at time t there is a liquid-

ity taker of H or N, where the columns are separated based on the time t liquidity

36


37/66

Table 12: Trade Frequency Conditional on Previous Trade. Panel A reports the un-

conditional frequency of observing HFT and non-HFT trades. Panel B reports the con-ditional frequency of observing HFT and non-HFT trades after observing trades of other

participants. In column and row headings t index trades. Panel C provides conditional

probabilities based on the previous trades size and participant. The first letter in the rows

for Panel A and B is who is demanding liquidity at Time t-1. The second letter in these

two panels is who is demanding liquidity at time t.

Panel A

T-1 Type and T Type %

HH 24.4%HN 25.8%

NH 26.8%

NN 23.0%

Total 100.0%

Panel B

T-1 Buy or Sell and T Buy or Sell

T-1 Type and T Type BB BS SB SS Total

% % % % %

HH 44.3% 5.9% 5.9% 43.9% 100.0%HN 44.1% 6.5% 6.3% 43.1% 100.0%

NH 41.9% 7.5% 7.7% 42.9% 100.0%

NN 41.5% 7.7% 7.8% 42.9% 100.0%

Total 43.0% 6.9% 6.9% 43.2% 100.0%

Panel C

LD Size

lag LD Size H1 H2 H3 H4 H5 N1 N2 N3 N4 N5 Total

% % % % % % % % % % %

H1 25.9% 32.2% 13.3% 2.5% 1.0% 7.5% 10.8% 5.4% 0.8% 0.4% 100.0%H2 5.1% 58.2% 14.8% 3.8% 1.6% 1.3% 11.4% 3.0% 0.7% 0.3% 100.0%

H3 3.2% 23.1% 46.2% 6.1% 2.3% 0.9% 4.3% 12.0% 1.3% 0.5% 100.0%

H4 1.9% 18.2% 18.7% 35.0% 7.6% 0.5% 2.9% 4.5% 8.6% 2.1% 100.0%

H5 1.7% 17.0% 16.2% 17.3% 27.8% 0.5% 2.7% 3.9% 5.2% 7.6% 100.0%

N1 6.8% 7.4% 3.5% 0.7% 0.3% 39.6% 29.5% 9.6% 1.7% 0.8% 100.0%

N2 1.7% 11.5% 2.8% 0.7% 0.3% 5.3% 57.9% 14.5% 3.6% 1.8% 100.0%

N3 1.3% 4.6% 12.4% 1.6% 0.6% 2.7% 23.1% 44.8% 6.0% 2.7% 100.0%

N4 0.6% 3.4% 3.9% 9.0% 2.5% 1.5% 17.8% 18.6% 34.5% 8.1% 100.0%

N5 0.7% 3.7% 4.0% 4.8% 7.9% 1.5% 18.3% 18.0% 17.3% 23.9% 100.0%

Total 3.7% 23.9% 15.4% 5.1% 2.3% 4.2% 23.6% 14.9% 4.8% 2.2% 100.0%37


38/66


39/66

Table 13: Average Time Between Trades. All values are in seconds. Panel A reports

the average amount of time between two trades, two HFT liquidity demanding trades,

and two non-HFT liquidity demanding trades, and between a trade where the initial trade

had a HFT, or a non-HFT liquidity demander. Panel B provides the average amount of

time between two different trade orderings and trade-size categories (refer to the previous

table for the different trade-size categories) The first two columns in Panel B is for some

trade type at t-1 and at time t there is a liquidity taker of H or N, where the columns are

separated based on the time t liquidity taker. The last two columns is similar except that

its columns are distinguished based on the time it takes when the time t-1 liquidity taker

is a certain type (H or N).

Panel A

HFT Non-HFT

Unconditional Time Between Trades 3.351 5.667

Time Between Trades of Same Type of Trader 8.696 9.081

Panel B

Time t Liquidity Taker Time t-1 Liquidity Taker

HFT Non-HFT HFT Non-HFT

S1 30.746 25.449 18.384 35.843

S2 9.620 10.578 7.582 12.657S3 5.069 5.513 4.485 6.134

S4 3.426 3.354 2.742 4.067

S5 4.576 4.065 3.572 5.056

M1 0.988 1.538 1.183 1.378

M2 1.219 1.399 1.064 1.572

M3 1.095 1.435 1.112 1.434

M4 1.098 1.166 0.998 1.273

M5 1.136 0.989 0.851 1.290

L1 0.746 1.266 0.899 1.118

L2 1.135 1.119 0.841 1.447

L3 0.746 1.149 0.842 1.065

L4 0.780 0.724 0.668 0.833

L5 0.729 0.639 0.602 0.760

39


40/66

Figure 5 also looks at trades throughout the day, but only charts the percent of

dollar volume in which HFT are demanding liquidity (top graph) and supplyingliquidity (bottom graph). Again this shows that HFT significantly reduce both

their supply and their demand for liquidity at the start and end of trading hours.

Figure 4: Type of Liquidity Providers / Takers throughout the day. The figure shows

the make up of traders throughout the day. It shows that HFT tend to reduce their trading

activity at the opening and closing of the trading day. the first letter is the liquidity taker,

the second letter is the liquidity provider.

.2

.4

.6

.8

1

Stacked

PercentofTrades

9:43 11:6 12:30 1:53 3:16 4:40Time of Day

HH Transaction HN Transaction

NH Transaction NN Transaction

6.1.2 HFT Liquidity Supply

This section analyzes how HFT supply liquidity. I focus on the amount of liquid-

ity HFT supply. I show that, beyond supplying liquidity in 51.4% of all trades,

they also often supply the inside quotes throughout the day. I then consider the

determinants that determine which stocks, and on what days, do HFT provide

the inside quotes. Finally, I examine what the additional price impact would be

on stocks if HFT where not part of the book. There is a sizeable impact, which

shows the importance of HFT providing liquid markets.

6.1.2.1 HFT Time at Inside Quotes To begin analyzing HFTs role in pro-

viding liquidity in the stock market I look at the amount of time HFT supply the

inside bid or ask compared to non-HFT firms. For each stock, on each day, I take

40


41/66

Figure 5: HFT Liquidity Demander or Supplier throughout the day. The graph shows

the make up of HFT throughout the day. The first graphs shows the HFT demand for liq-

uidity throughout the day. The second graph shows the HFT supply of liquidity through-

out the day.

.3

.4

.5

.6

HFTPercentofLiquidityDemanded

9:43 11:6 12:30 1:53 3:16 4:40Time of Day

.35

.4

.45

.5

.55

.6

HFT

PercentofLiquiditySupplied

9:43 11:6 12:30 1:53 3:16 4:40Time of Day

41


42/66

the number of minutes HFT are providing the inside bid or ask and, either: (a)

subtract the number of minutes non-HFT are providing the best inside bid or ask(ties are dropped), these are the Minutes results, or (b), divide this value by the

total number of minutes where HFT and non-HFT did not have the same inside

quotes, these are the Percent results. The results are in Table 14.

Table 14 looks at, for the 120 stocks, whether the HFT provide more liquidity

than non-HFT traders by considering how often they are providing the inside quote

(bid or ask). The way the metric is constructed there are a total of 900 minutes

( 2*60*7.5) that a HFT could potentially be providing the inside quote. This is

twice as many minutes then what actually occur during the trading day. The table

is separated into two categories - the category HFT - is when the HFT provides

fewer inside quotes than the non-HFT for a stock on a given day; category HFT+ is when the HFT is more frequently the inside quote provider for a stock on

a given day. The reason to separate out the two types is that it may be that some

stocks HFT do not actively try and provide inside quotes for, thus just taking the

average across all stocks would underweight the liquidity they provide in stocks

for which they are activily trying to place competitive quotes. Table 14 has three

panels, and within each panel either a category called Minutes or Percent.

Panel A considers quotes for all stocks; Panel B considers quotes for stocks on

days they are below their average spread; and Panel C considers quotes for stocks

on days they are above their average spread. The Minutes results display the

number of minutes HFT provide the inside quotes more than non-HFT through

the following calculation: sum the number of minutes HFT provide the best bid

or ask, subtract the number of minutes non-HFT are providing the best inside bid

or ask, and drop ties. A problem with this is that since the ties will vary across

days and stocks, the Minutes approach does not necessarily capture the frequency

that HFT provide better inside quotes than non-HFT. The Percent results avoids

this issue by dividing the number of minutes HFT provide the best quotes by the

total number of minutes where HFT and non-HFT did not have the same inside

quotes.

It does not appear there is a significant difference between the stocks in which

HFT decide to place aggressive bid/ask orders and those in which it does not.

The very low value for the mean of Net - by itself may imply that the HFT do notattempt to match or out-price the quotes of non-HFT for some stocks. But looking

at the Percent data, shows that the Net - and Net + results are about equally

distant from .5. Thus, the Minutes Net - results must be biased downwards as

a result of a large number of periods where HFT and non-HFT provide the same

prices. Looking at the Panel A - Percent results, on average HFT provide the

42


43/66


44/66

Table 14: HFT Time at Best Quotes. This table reports the number of minutes HFT

are at the best bid or ask compared to non HFT. The remainder of time both HFT andnon-HFT are both at the best quotes is not considered. Panel A is for all stocks at all

times, Panel B is for days when the spread is below average for that stock, Panel C is for

days when the spread is above average.

Panel A All -Minutes

HFT mean min p25 p50 p75 max N

Net - -255.6 -779.7 -368.5 -190.3 -75.8 -0.4 353.0

Net + 65.8 0.1 14.3 55.1 94.0 343.0 242.0

Average -124.9 -779.7 -223.5 -41.2 33.1 343.0 595.0

-Percent

Net - 0.281 0.000 0.162 0.307 0.410 0.499 353.000

Net + 0.709 0.502 0.587 0.708 0.802 0.964 242.000

Average 0.455 0.000 0.272 0.446 0.668 0.964 595.000

Panel B Low Spread -Minutes

Net - -243.1 -779.7 -367.0 -183.0 -70.9 -0.4 187.0

Net + 67.7 0.1 17.5 58.6 94.0 319.8 125.0

Average -118.5 -779.7 -205.9 -40.4 39.8 319.8 312.0

-Percent

Net - 0.283 0.000 0.162 0.309 0.404 0.498 187.000

Net + 0.701 0.509 0.587 0.704 0.786 0.960 125.000

Average 0.451 0.000 0.267 0.435 0.650 0.960 312.000

Panel C High Spread -Minutes

Net - -269.8 -779.1 -401.2 -204.0 -84.9 -1.1 166.0

Net + 63.6 1.1 13.3 50.4 91.5 343.0 117.0

Average -131.9 -779.1 -227.1 -41.2 28.9 343.0 283.0

-Percent

Net - 0.278 0.000 0.158 0.296 0.415 0.499 166.000

Net + 0.717 0.502 0.593 0.714 0.814 0.964 117.000

Average 0.460 0.000 0.274 0.455 0.680 0.964 283.000

44


45/66

Table 15: Determinants of HFT Percent of Liquidity Supplying The dependent vari-

able is the ratio of number of minutes HFT provides the inside bid or ask divided by the

total number of minutes of when the inside bid and ask differ between HFT and non-HFT.

(1)

Economic Impact

Market Cap. 0.654

(15.05)Market / Book -0.163

(-4.72)

$ of Non HFT Volume -0.162

(-3.82)

Average Spread -0.165

(-4.90)

Average Depth -0.086

(-2.65)

Volatility -0.241

(-7.14)Autocorrelation -0.006

(-0.18)

# of Non HFT Trades 0.217

(4.28)

Constant

(-2.55)

Observations 590

Adjusted R2 0.410

Standardized beta coefficients; tstatistics in parentheses

p < 0.05,

p < 0.01,

p < 0.001

45


46/66


47/66

Table16:Liquid

ityBookImpact.Thistableloo

ksattheliquiditydepthofHFTandnon-HFTtradersbyanalyzingthe

priceimpactfordifferentsizefirmsifavaryingrang

eoftrade-sizesweretohitthebo

ok.Thetwo-columnwidelabels,Very

SmalltoLargerefertothefirmsize.Thecolumnlab

elDollarsisthedollardifferenceasaresultofHFTbeinginthema

rket.

ThecolumnlabelBasisisthepercentbasispointschangeinpriceasaresultofHFTb

einginthemarket.Thedifferentrows

representavaryingnumberofsharestraded.

TradeSize

Large

Medium

Small

VerySmall

All

Basis

Dollars

Basis

Dollars

Basis

Dollars

Bas

is

Dollars

Basis

Dollar

s

100

1.065

0.004

2.474

0.008

8.074

0.026

12.789

0.020

5.176

0.013

200

1.260

0.005

3.686

0.012

9.734

0.030

17.049

0.028

6.739

0.016

300

1.331

0.007

4.151

0.014

11.450

0.035

19.328

0.032

7.683

0.019

400

1.428

0.008

4.619

0.016

13.233

0.040

22.283

0.037

8.784

0.022

500

1.592

0.011

5.161

0.019

16.307

0.051

25.041

0.042

10.147

0.027

600

1.663

0.013

6.042

0.023

19.934

0.065

28.749

0.048

11.866

0.033

700

1.770

0.016

7.162

0.028

22.472

0.075

31.133

0.052

13.176

0.038

800

1.855

0.017

9.394

0.037

26.358

0.088

34.587

0.058

15.250

0.045

900

1.955

0.018

11.539

0.045

29.677

0.098

38.725

0.064

17.330

0.050

1000

2.036

0.019

13.204

0.052

33.324

0.108

42.900

0.072

19.352

0.056

47


48/66

and decomposes the variance of the common component of the price to attribute

contribution to the efficient price path between the two types of traders. The HFTprovide substantially more information to the price process than do non-HFT. The

Hasbrouck methodologies utilized in this paper are similar to those found in Hen-

dershott and Riordan (2009) and other papers.

6.2.1 Permanent Price Impact

To measure the information content of HFT and non-HFT trades I calculate the

permanent price impact of HFT and non-HFT trades. Hendershott and Riordan

(2009) performed a similar calculation for trader types looking at algorithmic

trading, while Barclay, Hendershott, and McCormick (2003) used the technique to

compare information from different markets. The HFT dataset is especially wellsuited for this as it is in milliseconds and thus avoids problems of multiple trades

occurring in one time period, as occurs with data denoted in seconds. I estimate

the model on a trade-by-trade basis using 10 lags for HFT and non-HFT trades. I

estimate the model for each stock for each day. As in Barclay, Hendershott, and

McCormick (2003) and Hendershott and Riordan (2009), I estimate three equa-

tions, a midpoint quote return equation, an HFT equation, and a non-HFT trade

equation. The time index, t, is based on event time, not clock time, and so eacht is an event that is a trade or quote change. qH is defined as the signed (+1 fora buy, -1 for a sell) HFT trades and qN is the similarly denoted signed non-HFTtrades. rt is defined as the quote midpoint to quote midpoint return between tradechanges. The 10-lag vector auto regression (VAR) is:

rt =10i=1

irti +10i=0

iqHti +

10i=0

iqNti + 1,t,

qHt =10i=1

irti +10i=0

iqHti +

10i=0

iqNti + 2,t,

qNt =10

i=1

irti +10

i=0

iqHti +

10

i=0

iqNti + 3,t.

After estimating the VAR model, I invert the VAR to get the vector moving

average (VMA) model to obtain:

48


49/66

rtqHtqNt

= a(L) b(L) c(L)d(L) e(L) f(L)g(L) h(L) i(L)

1,t2,t3,t

, (4)where the vectors a(L) - i(L) are lag operators. Hasbrouck (1991a) interprets

the impulse response function for HFT,10

t=0 b(L), as the private information con-tent of an innovation in HFT trades. The non-HFT impulse response function is10

t=0 c(L) and is the private information content of an innovation in non-HFTtrades. The impulse response function is a technology first used in the macro-

economic literature to determine the impact of an exogenous shock to the econ-

omy as it worked its way through the economy. Hasbrouck (1991a) and Has-

brouck (1991b) took this methodology and applied it to the microstructure litera-ture. The expected portion of a trade should not impact prices and so should not

show up in the impulse response function; however, the unexpected portion, the

innovation, of a trade should influence the price of future trades. The impulse

response function estimates this impact on future trades.

Table 17 shows the results of the HFT and non-HFT impulse response func-

tion for 10 events into the future. There are 105 firms presented as fifteen stocks

do not contain enough data to calculate the VAR. Each stock is reporte

hft trading

Documents